# grim: A Flexible, Conservative Scheme for Relativistic Fluid Theories

## TL;DR

The paper introduces grim, a flexible, conservative numerical code for simulating relativistic plasmas that incorporates dissipative effects like heat conduction and viscosity, applicable to complex astrophysical scenarios such as black hole accretion.

## Contribution

grim is a novel, physics-agnostic, and efficient code that unifies time evolution and primitive variable inversion, enabling advanced modeling of relativistic fluids with dissipation in both CPU and GPU environments.

## Key findings

- Successfully models classical and extended GRMHD test problems
- Captures shock substructure due to dissipation effects
- Simulates relativistic instabilities and accretion flows around black holes

## Abstract

Hot, diffuse, relativistic plasmas such as sub-Eddington black hole accretion flows are expected to be collisionless, yet are commonly modeled as a fluid using ideal general relativistic magnetohydrodynamics (GRMHD). Dissipative effects such as heat conduction and viscosity can be important in a collisionless plasma and will potentially alter the dynamics and radiative properties of the flow from that in ideal fluid models; we refer to models that include these processes as Extended GRMHD. Here we describe a new conservative code, grim, that enables all the above and additional physics to be efficiently incorporated. grim combines time evolution and primitive variable inversion needed for conservative schemes into a single step using an algorithm that only requires the residuals of the governing equations as inputs. This algorithm enables the code to be physics agnostic as well as flexibility regarding time-stepping schemes. grim runs on CPUs, as well as on GPUs, using the same code. We formulate a performance model, and use it to show that our implementation runs optimally on both architectures. grim correctly captures classical GRMHD test problems as well as a new suite of linear and nonlinear test problems with anisotropic conduction and viscosity in special and general relativity. As tests and example applications, we resolve the shock substructure due to the presence of dissipation, and report on relativistic versions of the magneto-thermal instability and heat flux driven buoyancy instability, which arise due to anisotropic heat conduction, and of the firehose instability, which occurs due to anisotropic pressure (i.e. viscosity). Finally, we show an example integration of an accretion flow around a Kerr black hole, using Extended GRMHD.